Problem: John Doe has an n × m table. John Doe can paint points in some table cells, not more than one point in one table cell. John Doe wants to use such operations to make each square subtable of size n × n have exactly k points.

John Doe wondered, how many distinct ways to fill the table with points are there, provided that the condition must hold. As this number can be rather large, John Doe asks to find its remainder after dividing by 1000000007 (109 + 7).

You should assume that John always paints a point exactly in the center of some cell. Two ways to fill a table are considered distinct, if there exists a table cell, that has a point in one way and doesn't have it in the other.

Input

A single line contains space-separated integers n, m, k (1 ≤ n ≤ 100; n ≤ m ≤ 1018; 0 ≤ k ≤ n2) — the number of rows of the table, the number of columns of the table and the number of points each square must contain.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. 

Output

In a single line print a single integer — the remainder from dividing the described number of ways by 1000000007 (109 + 7).

Examples

Input

5 6 1


Output

45

Note

Let's consider the first test case: 

<image> The gray area belongs to both 5 × 5 squares. So, if it has one point, then there shouldn't be points in any other place. If one of the white areas has a point, then the other one also must have a point. Thus, there are about 20 variants, where the point lies in the gray area and 25 variants, where each of the white areas contains a point. Overall there are 45 variants.

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Round144B {

	public static long mod = (long)1e9+7;
	public static long[] fact;
	public static long[] invfact;
	
	public static long nCr(int n, int r) {
		return (((fact[n] * invfact[r])%mod) * invfact[n - r])%mod;
	}
	
	public static int max = 110;
	public static long[][] dp;
	public static long[][] pre;
	public static int n;
	public static long m;
	
	public static void solve() {
		fact = new long[max];
		invfact = new long[max];
		fact[0] = invfact[0] = 1;
		for(int i = 1; i < max; i++) {
			fact[i] = fact[i - 1] * i;
			fact[i] %= mod;
			invfact[i] = invfact[i - 1] * ModInverse(i, mod);
			invfact[i] %= mod;
		}
		n = s.nextInt();
		m = s.nextLong();
		pre = new long[n + 1][n + 1];
		for(int i = 1; i < n + 1; i++) {
			for(int j = 0; j < n + 1; j++) {
				pre[i][j] = fast(nCr(n, j), ((m - i)/(long)n) + 1);
			}
		}
		dp = new long[max][max * max];
		for(int i = 0; i < max; i++) {
			Arrays.fill(dp[i], -1);
		}
		int k = s.nextInt();
		long ans  = Recur(1, k);
		out.println(ans);
	}
	
	public static long Recur(int pos, int left) {
		if(left == 0) {
			return 1;
		}
		if(pos == n + 1) {
			return 0;
		}
		if(dp[pos][left] != -1) {
			return dp[pos][left];
		}
		long ans = 0;
		for(int i = 0; i <= Math.min(left, n); i++) {
			ans += (Recur(pos + 1, left - i) * pre[pos][i])%mod;
			if(ans >= mod) ans -= mod;
		}
		return dp[pos][left] = ans;
	}
	
	public static long fast(long a, long n) {
		if(n == 1) {
			return a;
		}
		long ans = fast(a, n/2L);
		ans = (ans * ans);
		ans %= mod;
		if(n%2 == 1) {
			ans = ans * a;
			ans %= mod;
		}
		return ans;
	}

	public static void main(String[] args) {
		out = new PrintWriter(new BufferedOutputStream(System.out));
		s = new FastReader();
		solve();
		out.close();
	}
	
	public static class Triplet {
		long gcd;
		long x;
		long y;

		Triplet(long gcd, long x, long y) {
			this.gcd = gcd;
			this.x = x;
			this.y = y;
		}
	}

	public static Triplet ExtendedEuclideanAlgo(long a, long b) {
		if (a == 0) {
			return new Triplet(b, 0, 1);
		}
		Triplet ans = ExtendedEuclideanAlgo(b % a, a);
		long x = ans.y - (b / a) * ans.x;
		long y = ans.x;
		return new Triplet(ans.gcd, x, y);
	}

	public static long ModInverse(long a, long m) {
		Triplet ans = ExtendedEuclideanAlgo(a, m);
		if (ans.gcd != 1) {
			//System.out.println("Multiplicative inverse doesnot exist");
			return -1;
		} else {
			//m is added to handle negative x
			long result = (ans.x % m + m) % m;
			return result;
		}
	}

	public static FastReader s;
	public static PrintWriter out;

	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	
}